Properties

Label 1600r
Number of curves 4
Conductor 1600
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("1600.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1600r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1600.w3 1600r1 [0, -1, 0, -133, -363] [2] 384 \(\Gamma_0(N)\)-optimal
1600.w4 1600r2 [0, -1, 0, 367, -2863] [2] 768  
1600.w1 1600r3 [0, -1, 0, -4133, 103637] [2] 1152  
1600.w2 1600r4 [0, -1, 0, -3633, 129137] [2] 2304  

Rank

sage: E.rank()
 

The elliptic curves in class 1600r have rank \(0\).

Modular form 1600.2.a.w

sage: E.q_eigenform(10)
 
\( q + 2q^{3} + 2q^{7} + q^{9} + 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.